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The packets in a data network follow different paths from source to destination and the possible longest path traversed by a packet in a network having n nodes is (n-1). This is termed as the worst case condition and the route followed is called the critical path. The critical paths increase transmission delay, cost, network traffic etc, thus degrades the network performance. In order to preserve the performance, this paper proposes a greedy technique to minimize the length of the critical paths by removing one or more link(s) in such a fashion that the reliability of the original network is minimally reduced. This has been done by iteratively removing one link from the critical path and measuring the reliability in each case and finally the link(s) corresponding to minimum change in reliability is removed. As an illustration, the proposed method has been applied in a data network of 5 nodes and 8 links, and the results obtained are given, which are satisfactory.